N-Symmetric Interaction of N Hetons, II: Analysis of the Case of Arbitrary N

Abstract

This paper seeks and examines N-symmetric vortical solutions of the two-layer geostrophic model for the special case when the vortices (or eddies) have vanishing summed strength (circulation anomaly). This study is an extension [Sokolovskiy et al. Phys. Fluids 2020, 32, 09660], where the general formulation for arbitrary N was given, but the analysis was only carried out for N=2. Here, families of stationary solutions are obtained and their properties, including asymptotic ones, are investigated in detail. From the point of view of geophysical applications, the results may help interpret the propagation of thermal anomalies in the oceans.